Research And Implementation Of LWE Public-key Encryption Scheme

With the rapid development of network technologies, people pay more and more attention to information security problems, and this is why the encryption technologies develop so fast. At the moment there are mainly two kinds of encryption technologies, the symmetric encryption technology and the public key encryption technology.Due to its high security level and convenient key management, public key encryption technology is favored by more and more researchers.Currently popular public key encryption schemes are RSA and ECC, which have been applicated in some areas.Though lattice- based LWE public key encryption schemes are still on theoretical research, compared with RSA, ECC, LWE schemes have the advantange of simple circuit realization, high security level for quantum attack assistance, which are of great potential for hardware ecncryption applications.In this paper, two kinds of LWE public key encryption schems are studied from the view of hardware application and its circuits are designed. At first, the paper analyzes the adavatages and disadvantages of Regev LWE schemes and R-LWE schems, and predicts the hardware performance of the two schemes. Both of the cryptographies are simple for hardware implementation, and of high security for its rejection against quantum attack. The strength of Regev LWE is the simple arithmetic; the defect is the too long public key size. R-LWE has good overall performance, the public key size is short, and the encryption efficiency is high. The only defect is that the algorithm involves in ring polynomial multiplication, so R-LWE scheme is a little complex than the Regev LWE scheme.Then, to improve the defect that the public key size of Regev LWE scheme is too large, the paper proposes a method which uses a public key operating circuit to replace memory circuit. Whith only several additional LFSRs and combinational logic circuits, the memory space for public key is reduced by 90%. To improve the defect that the ring polynomial multiipication is too complex, the paper adopts a method which performs fast number theoretic transform for the input sequence. In this way, the time complexity of the multiplication operation is reduced from ? 2O(n) to ?O(nlog n).Finally, the paper designs and realizes the Regev LWE encryption circuit and the R-LWE encryption circuit. The simulation results of the designed circuits show that the two circuits achieve desired functions. And according to the synthesis reports, Regev LWE circuit consumes a little logical resource, only 202 slices are used, however, the memory resource is still very large with around 160 kbits space. R-LWE circuit consumes 668 slices, and the memory space is around 10 kbits. Though the public key size of Regev LWE scheme is very large which is unreasonable for hardware application, R-LWE scheme performs very well in circuit resource, security level and encryption effectioncy, even better than RSA scheme in some aspects. As a result, lattice-base LWE public-key encryption schemes are of great potential for hardware encryption applications.